Searching the possibility of $a_0(1450)$ scalar state being a diquark structure via charmed meson semileptonic decays

Abstract

The internal structure of light scalar state $a_0(1450)$ has not been definitively determined, it may consist of multiple possible states. Among them, it has the possibility of being regarded as a diquark state. Based on this possibility, we use QCD light-cone sum rules to study the semileptonic decay process $D \to a_0(1450)\ell ν_\ell $ with $\ell=(e, μ)$ to verify its rationality. Firstly, we construct two types of twist-2 light-cone distribution amplitude schemes based on the light-cone harmonic oscillator model, and present their moments $\langleξ^{n}\rangle |_μ$ and Gegenbauer moments $a_{n}(μ)$ at $μ_0=1~{\rm GeV}$ and $μ_k= 1.4~{\rm GeV}$ for $n=(1,3,5)$. In the large recoil region, we obtain the transition form factors (TFFs): $f_+^{\rm (S1)}(0) = 0.836_{-0.116}^{+0.119}$, $f_+^{\rm (S2)}(0)=0.767_{-0.105}^{+0.106}$ and $f_-(0)=0.630_{-0.077}^{+0.078}$. A simplified series expansion $z(q^2, t)$ is used to extrapolate TFFs to the entire physical $q^2$-region. For $q^2=10^{-5} ~{\rm GeV}^2$, we compute angular distribution of the differential decay width ${dΓ}/{d\cosθ_\ell }$ over the range $\cosθ_\ell \in [-1,1]$. Subsequently, we obtain differential decay widths and branching fractions for $D^0 \to a_0(1450)^- \ell^+ ν_\ell $ and $D^- \to a_0(1450)^0 \ell^- \barν_\ell $, where the branching fractions being of order $10^{-6}$. Finally, we analyze three angular observables for the semileptonic decay process $D^- \to a_0(1450)^0 \ell^- \barν_\ell $, the forward-backward asymmetry ${\cal A}_{\rm FB}$, lepton polarization asymmetry ${\cal A}_{λ_\ell}$ and $q^2$-differential flat term~${\cal F}_{\rm H}$.